Put spinach, oysters and their liquor, clam juice, garlic, and pepper to taste into a medium nonreactive pot over medium-high heat. Bring to a simmer, breaking up spinach with the back of a spoon, and simmer until heated through, about 5 minutes. Transfer to a blender and puree until very smooth. Set spinach and oyster mixture aside.

Preheat broiler. Bring half-and-half to a simmer in a medium pot over medium heat. Whisk in butter, then spinach and oyster puree, and return to a simmer. Add steak sauce, Tabasco, Worcestershire, and salt to taste. Dissolve cornstarch in 1 tablespoon water, then whisk into soup. Keep soup warm over lowest heat.
Whisk cream in a bowl until soft peaks form. Divide soup between 4 shallow heatproof soup bowls and put a big spoonful of the whipped cream on top of each. Place bowls of soup under broiler briefly to brown cream, then serve soup immediately.